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- W2024452216 abstract "The dual variety X * for a smooth n-dimensional variety X of the projective space PN is the set of tangent hyperplanes to X. In the general case, the variety X * is a hypersurface in the dual space (PN)*. If dim X *<N−1, then the variety X is called dually degenerate. The authors refine these definitions for a variety X⊂PN with a degenerate Gauss map of rankr. For such a variety, in the general case, the dimension of its dual variety X * is N−l−1, where l=n−r, and X is dually degenerate if dim X *<N−l−1. In 1979 Griffiths and Harris proved that a smooth variety X⊂PN is dually degenerate if and only if all its second fundamental forms are singular. The authors generalize this theorem for a variety X⊂PN with a degenerate Gauss map of rankr." @default.
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- W2024452216 date "2005-05-01" @default.
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- W2024452216 title "Dually Degenerate Varieties and the Generalization of a Theorem of Griffiths?Harris" @default.
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- W2024452216 doi "https://doi.org/10.1007/s10440-004-7029-7" @default.
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